This program will display the real and imaginary roots for a polynomial of the form f(x)=A0+A1*x+A2*x^2+...

Forget Newton and Half-Int.  They were simply programming problems.  If you have a polynomial to solve, this is the program that will do it.

Downloads:

Liberty Basic 2 program - bairstow.bas

Smallbasic program - sb_bairstow.bas

Test case:

real and imaginary roots of polynomials
using bairstow's method
form is y=A0+A1*x+A2*x^2+A3*x^3+....

degree of polynomial: 4

coefficent of A(0)=  12
coefficent of A(1)=  -19
coefficent of A(2)=  12
coefficent of A(3)=  -6
coefficent of A(4)=  1

Roots:

0.5 + I * 1.6583124
0.5 - I * -1.6583124

4.0
1.0